Answer: the function g(x) has the smallest minimum y-value.
Explanation:
1) The function f(x) = 3x² + 12x + 16 is a parabola.
The vertex of the parabola is the minimum or maximum on the parabola.
If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.
The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.
When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).
Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.
Then, finding the minimum value of the function is done by finding the vertex.
I will change the form of the function to the vertex form by completing squares:
Given: 3x² + 12x + 16
Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4
That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).
Then the minimum value is 4 (when x = - 2).
2) The othe function is <span>g(x)= 2 *sin(x-pi)
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The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.
When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2
Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.
Answer:
The correct scientific notation for the number 500.0 is 
Step-by-step explanation:
While writing a large number in scientific notation we do below mentioned two things.
- We take any number between 1 and 10
- Then we multiply this number with an exponent of 10.
Hence, any number in scientific notation is in the form 
Here a is any number between 1 and 10.
b is exponent of 10.
Now, writing 500 in scientific notation, we take a = 5
Hence, we have to take b = 2, since 5 multiplied by 100 equas 500.
Thus, we have
Answer:
Isosceles Triangle; Acute Triangle
Step-by-step explanation:
Review your definitions of the different types of triangles:
acute triangle- a triangle that has three acute (less than 90 degrees) angles
obtuse triangle- a triangle that has an obtuse (greater than 90 degrees) angle.
right triangle- a triangle that had one right (90 degrees) angles
isosceles triangle- a triangle with two congruent sides and one unique side and angle.
equilateral triangle- a triangle with three congruent sides and three congruent angles.
scalene triangle- a triangle with no congruent sides and no congruent angles.
With these definitions, we can classify ΔPQR as an isosceles acute triangle.
Half a book each month!!! have a good day!
Choice A is false because they are rounding to the nearest tenth (one decimal place) and not nearest hundredth (two decimal places)
Choice B is false as well because 3.825 should round to 3.83. The 5 at the end tells you to round up.
Choice C is false too. The value 3.824 should round to 3.82. Not sure how they got 3.81, so it seems like a deliberate trick question or silly answer.
Choice D is true. The three decimal values are rounded properly to the correct number of decimal places.
Therefore choice D is the answer
